2(x+3)3(x-5)=8(x-6)

Solution for 2(x+3)3(x-5)=8(x-6) equation:

Simplifying
2(x + 3) * 3(x + -5) = 8(x + -6)

Reorder the terms:
2(3 + x) * 3(x + -5) = 8(x + -6)

Reorder the terms:
2(3 + x) * 3(-5 + x) = 8(x + -6)

Reorder the terms for easier multiplication:
2 * 3(3 + x)(-5 + x) = 8(x + -6)

Multiply 2 * 3
6(3 + x)(-5 + x) = 8(x + -6)

Multiply (3 + x) * (-5 + x)
6(3(-5 + x) + x(-5 + x)) = 8(x + -6)
6((-5 * 3 + x * 3) + x(-5 + x)) = 8(x + -6)
6((-15 + 3x) + x(-5 + x)) = 8(x + -6)
6(-15 + 3x + (-5 * x + x * x)) = 8(x + -6)
6(-15 + 3x + (-5x + x2)) = 8(x + -6)

Combine like terms: 3x + -5x = -2x
6(-15 + -2x + x2) = 8(x + -6)
(-15 * 6 + -2x * 6 + x2 * 6) = 8(x + -6)
(-90 + -12x + 6x2) = 8(x + -6)

Reorder the terms:
-90 + -12x + 6x2 = 8(-6 + x)
-90 + -12x + 6x2 = (-6 * 8 + x * 8)
-90 + -12x + 6x2 = (-48 + 8x)

Solving
-90 + -12x + 6x2 = -48 + 8x

Solving for variable 'x'.

Reorder the terms:
-90 + 48 + -12x + -8x + 6x2 = -48 + 8x + 48 + -8x

Combine like terms: -90 + 48 = -42
-42 + -12x + -8x + 6x2 = -48 + 8x + 48 + -8x

Combine like terms: -12x + -8x = -20x
-42 + -20x + 6x2 = -48 + 8x + 48 + -8x

Reorder the terms:
-42 + -20x + 6x2 = -48 + 48 + 8x + -8x

Combine like terms: -48 + 48 = 0
-42 + -20x + 6x2 = 0 + 8x + -8x
-42 + -20x + 6x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-42 + -20x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + -10x + 3x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-21 + -10x + 3x2)' equal to zero and attempt to solve:

Simplifying
-21 + -10x + 3x2 = 0

Solving
-21 + -10x + 3x2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-7 + -3.333333333x + x2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -3.333333333x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + -3.333333333x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -3.333333333x + x2 = 0 + 7
-3.333333333x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
-3.333333333x + x2 = 7

The x term is -3.333333333x.  Take half its coefficient (-1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
-3.333333333x + 2.777777779 + x2 = 7 + 2.777777779

Reorder the terms:
2.777777779 + -3.333333333x + x2 = 7 + 2.777777779

Combine like terms: 7 + 2.777777779 = 9.777777779
2.777777779 + -3.333333333x + x2 = 9.777777779

Factor a perfect square on the left side:
(x + -1.666666667)(x + -1.666666667) = 9.777777779

Calculate the square root of the right side: 3.12694384

Break this problem into two subproblems by setting 
(x + -1.666666667) equal to 3.12694384 and -3.12694384.

Subproblem 1
x + -1.666666667 = 3.12694384

Simplifying
x + -1.666666667 = 3.12694384

Reorder the terms:
-1.666666667 + x = 3.12694384

Solving
-1.666666667 + x = 3.12694384

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + x = 3.12694384 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + x = 3.12694384 + 1.666666667
x = 3.12694384 + 1.666666667

Combine like terms: 3.12694384 + 1.666666667 = 4.793610507
x = 4.793610507

Simplifying
x = 4.793610507

Subproblem 2
x + -1.666666667 = -3.12694384

Simplifying
x + -1.666666667 = -3.12694384

Reorder the terms:
-1.666666667 + x = -3.12694384

Solving
-1.666666667 + x = -3.12694384

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + x = -3.12694384 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + x = -3.12694384 + 1.666666667
x = -3.12694384 + 1.666666667

Combine like terms: -3.12694384 + 1.666666667 = -1.460277173
x = -1.460277173

Simplifying
x = -1.460277173

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.793610507, -1.460277173}
Solution
x = {4.793610507, -1.460277173}